Question

If 2x + 3y = 12 and xy = 6, find the value of 8x³+ 27y³​

Answer 1

Answer:

Answer is 432.

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Step-by-step explanation:

Answer 2

Question

If $2x+3y=12$ and $xy=6$, find the value of $8x^{3}+27y^{3}$.

Solution

The value to find is $8x^{3}+27y^{3}=(2x)^{3}+(3y)^{3}$.

If we factorize the value to find we get $(2x+3y)(4x^{2}-6xy+9y^{2})$.

The value of the first factor $(2x+3y)=\boxed{12}$.

The value of the second factor $(4x^{2}-6xy+9y^{2})$

$=(2x+3y)^{2}-3\cdot 6xy$

$=12^{2}-3\cdot 6\cdot 6$

$=144-108=\boxed{36}$.

The product of two factors $12\cdot 36=\boxed{432}$.